OpenAI has spent the last few years planting flags across the increasingly difficult terrain in mathematics. This week, it claimed one of its biggest prizes yet: a solution to a legendary Millennium Prize problem. In normal circumstances, this would have been celebrated as a historic achievement.

Instead, many mathematicians have watched OpenAI’s relentless advance with growing unease. To them, the company appears less like an enthusiastic newcomer than an impossibly well-resourced interloper, charging into problems they have dedicated their lives to studying with little apparent regard for long-standing norms or the consequences for those left in its wake. At the heart of that unease is a sense that OpenAI is doing mathematics for different reasons. Mathematicians want to advance the field. OpenAI wants to win.  

This week, The Verge spoke with more than a dozen mathematicians, including Tristan Buckmaster and Andreas Thom, who are at the center of recent controversies surrounding OpenAI’s work in the field. Even those skeptical of the most serious allegations described a field shaken by the tech giant’s conduct and fearful of what it might do next in its determination to trounce its rivals.

Buckmaster has accused OpenAI of failing to adequately explain whether work he did through its tool Codex could have contributed to its recent successes. In a statement to The Verge, OpenAI spokesperson Laurance Fauconnet strenuously denied that material from his prompts had played a role: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.”

Buckmaster remains unconvinced. “Given their behavior up until this point, one should take such statements with great skepticism,” he said.

Mathematics is not normally this dramatic, so how did things get this bad? A rumor was all it took for tensions to boil over. 

OpenAI says it heard some researchers were making progress on Millennium Prize problems and decided to see whether one of its advanced, unreleased models could make headway too. It turns out it could. OpenAI says it took roughly 10,000 agents, tens of millions of dollars of compute, and just 88 hours to find a solution to the Navier-Stokes problem, which concerns the flow of fluids.

The company had also discovered who it was racing against: Buckmaster, an NYU professor, and Levent Alpöge, a researcher at one of its fiercest rivals, Anthropic. Among several lines of research, the pair were pursuing Navier-Stokes, though had not yet completed a proof. Some details of what happened next are fiercely contested, but the two sides broadly agree on the basic sequence of events. One thing is particularly clear: Alpöge’s involvement was a problem for OpenAI, despite his saying it was a “personal collaboration” independent of his work with Anthropic. 

Buckmaster said he contacted OpenAI after learning the company had become aware of their progress and was racing toward a solution of its own. He said discussions with OpenAI researcher Sébastien Bubeck grew contentious and, in his view, threatening, but the company offered a path forward for him — one that excluded Alpöge. Buckmaster said he was offered practically “unlimited compute” to finish his own work, and the opportunity to be the sole author of OpenAI’s paper announcing the breakthrough, which would of course credit its tools. 

“All I had to do was throw Levent under the bus,” Buckmaster told The Verge in a phone interview. He said he flatly rejected Bubeck’s offer, which he viewed as a “bribe,” and also began questioning whether OpenAI may have benefited from his use of Codex, one of the company’s AI tools he had been using to tackle the problem. OpenAI has denied that anyone — or any agent — accessed his specific user data, and until its more recent comments acknowledged it could not rule out the possibility data derived from his use of the products was used to improve the model.  

Buckmaster ultimately decided to go public with both his work and his account of OpenAI’s conduct. His office, he said, had been transformed into something of a “war room,” with colleagues helping scrutinize his mathematics, coordinate outreach, and even get in touch with lawyers. 

Bubeck has rejected Buckmaster’s characterization of the conversations on social media and in an interview with The New York Times. He acknowledged offering OpenAI’s resources to help Buckmaster complete his own proof or to have him take over the writing of the company’s. Strikingly, Bubeck said OpenAI had made similar arrangements with other mathematicians, though did not identify them. 

But his account nevertheless makes clear that Alpöge’s affiliation with Anthropic was a sticking point. “From our perspective, how can we have an internal OpenAI project with an Anthropic employee?” he told the Times.

If the goal is to compete in mathematics, there are few bigger trophies than solving a Millennium Prize problem. The seven problems, set out by the Clay Mathematics Institute in 2000, are widely considered among the most formidable challenges in the field. Each carries a $1 million bounty for whoever solves it. Many had already endured decades of intense scrutiny by the time the prizes were established. In the quarter-century since, only one — the Poincaré conjecture, a topological problem concerning three-dimensional spheres — has fallen. 

For an AI company looking to prove that its models are the best at mathematics, then, they are irresistible targets. To Buckmaster and many other mathematicians The Verge spoke to, that helps explain why OpenAI moved so ferociously when it heard others were closing in — particularly once a rival AI company appeared to be involved. 

For Buckmaster, the episode reinforced something he already believed strongly from a previous spell collaborating with Google DeepMind: “All these tech people are obsessed” with solving big famous problems and are “obsessed with scooping,” he said. “Its all about competition.”

He said what often gets “lost” when companies race to solve famous problems are the mathematicians themselves — not just the people whose accumulated work makes these breakthroughs possible, but the reasons they do mathematics to begin with. Yes, some may pursue prestige, but most are simply not trophy hunters. Andras Juhasz, a professor of mathematics at the University of Oxford, described mathematics as an elegant discipline that is part science, part art, with many different motivations driving those working there. “Often there is no immediate practical application,” he said. “They do it because it’s beautiful. They enjoy it. It’s the sense of discovery. It’s natural.” 

Unlike classroom-level mathematical exercises, frontier mathematics rarely has a prescribed route to an answer. Researchers can attack problems from any number of angles, some radically different, which makes the ideas that lead to a solution — and who developed them — especially important, perhaps more so than solving a problem itself. Mathematicians care deeply about this lineage because it is how the field expands, with new techniques and methods often proving more consequential than the problem they were designed to solve. 

To Buckmaster, his exchanges with Bubeck typify the chasm that separates the worlds of research mathematics and Big Tech, and highlight the differences between what is considered valuable in research. Reading from notes he took while chatting with Bubeck, he said the OpenAI researcher was visibly taken aback when he rejected the company’s offer to take credit. “I could see Sébastien’s face. He was shocked when I said I don’t care about the Millennium Prize,” he recalled.

Buckmaster said he had encountered a similar mentality among tech researchers before. In that world, he said there is an intense fixation on prestige, fame, being first, and being seen to be first. “That’s the only currency,” he said. 

Buckmaster isn’t the only mathematician to come away from an encounter with OpenAI concerned about the company’s motivations. Andreas Thom, a professor at the Technical University of Dresden in Germany, found himself at the center of a controversy last month after OpenAI announced an impressive mathematical result that built heavily on work by him and fellow researcher Gábor Kun. The company quietly amended its announcement to acknowledge the pair’s contribution without announcing or publicly disclosing the change. 

Thom described the ordeal as “not a very pleasant experience,” but told The Verge he had largely put it behind him until Buckmaster went public. His allegations prompted Thom to revisit an unresolved question about OpenAI’s breakthrough: whether conversations he and his colleagues had with ChatGPT about the research could have been used to help improve the models that ultimately cracked the problem he’d spent years working on. 

Only OpenAI has the information needed to answer that question, Thom said. “To be honest, I suspect that they don’t even know.” The people training the models and using them to produce mathematical results are “a different kind of people,” he said. To him, that’s hardly an excuse for the uncertainty. “Because it effectively means that they don’t really care, right?”

The tension echoes fights already playing out elsewhere. Writers, musicians, artists, and media companies have all challenged AI companies over systems built from vast stores of human-created work, often without permission, recognition, or compensation. While mathematics may seem a world apart, the underlying question is the same: What do companies owe to the people whose accumulated work they ingested to build their systems? 

In Thom’s case, the question remains unresolved. OpenAI did not respond to The Verge’s question on whether data from conversations Thom and his colleagues had with ChatGPT could have contributed to the company’s solution that built on his work.

More broadly, Thom said he resents what he sees as a failure to recognize the “the communal effort that this entire community has put into all the research results” underpinning AI’s recent mathematical advances. Companies, he said, “are just now using [it] as if it was kind of nothing.” 

“I think there is a certain attitude that I don’t like in that,” he said. 

It’s not that mathematicians are strangers to competition — researchers care deeply about priority and bitter disputes over who came first litter mathematical history — but while competition does not preclude cooperation, these are no ordinary competitors. Scooping in mathematics has historically been relatively difficult for obvious reasons: Very few people have the specialized expertise to swoop in on a discovery at speed. AI companies operate on a different scale. Researchers worry they could turn scooping into something of an industrial process mathematicians would have little chance of fighting back against, rapidly spinning up thousands upon thousands of agents and enormous amounts of compute whenever word spreads that a breakthrough is close.

To Buckmaster, OpenAI could have easily collaborated with researchers rather than race them to results. Indeed, the company seemed perfectly willing to work with him. The problem was Alpöge, or, more specifically, his ties to Anthropic.

“They were in such a rush to publish, to beat Anthropic,” he said. They barely took note of the researchers caught in the middle.

For all the rush, OpenAI won’t know whether it has won the Millennium Prize for solving Navier-Stokes for years. The Clay Mathematics Institute requires a period of two years to have passed since a result was published, during which it must have “received general acceptance in the global mathematics community.” For now, Navier-Stokes occupies a peculiar limbo: The Institute has removed it from its list of unsolved problems, though hasn’t yet declared it solved. “The process is deliberately unhurried,” the Institute said in a statement.   

OpenAI, meanwhile, has already moved on. In a statement to The Verge, OpenAI’s Fauconnet said that “since the completion of Navier-Stokes we have made substantial progress on another Millennium Prize problem,” adding that the company is “working through how to share these results thoughtfully.”

Which problem remains unclear. Unconfirmed speculation on social media suggests this could be the Hodge conjecture, which concerns, very roughly speaking, how complex geometric shapes can be understood in terms of simpler building blocks. Rumors are also circulating that Anthropic is closing in on a Millennium Prize problem of its own.

As the two giants of AI race to collect yet more mathematical trophies, they are discovering that astonishing results alone are not enough to earn the trust of the community they are transforming.

Mathematicians are beginning to push back. Many The Verge spoke to, even the most enthusiastic proponents of AI in the field, worried the companies were having a chilling effect on research, pushing mathematicians to be more secretive about unfinished work for fear someone may swoop in and beat them to it. Several said colleagues who had previously compiled lists of important unsolved problems were reconsidering the practice, concerned that what was intended as a useful resource for the field could instead become a list of targets for AI companies. 

Resistance is becoming increasingly public. In June, mathematicians published the Leiden Declaration, a set of principles for the responsible use of AI in mathematics that has been endorsed by the International Mathematical Union and signed by nearly 3,900 people, an increase of nearly 500 people since I last covered it in mid-August. It urges policymakers, governments, the media, and other groups to not buy into “the hype” created by companies who “overstate the capabilities of their products.” As the Millennium Prize controversy raged, OpenAI withdrew its sponsorship of an undergraduate mathematics hackathon at Caltech following fierce opposition decrying the intrusion of corporate interests and worries the event would create a deluge of low-quality “slop mathematics.” 

Shing-Tung Yau, a professor of mathematics at China’s Tsinghua University, an emeritus professor at Harvard, and a recipient of the prestigious Fields Medal, told The Verge he worries about the potential effect on young researchers. “Working on hard problems already carries considerable risk for Ph.D. students and junior faculty,” he said. “The prospect of competing with powerful AI companies, whose resources far exceed those available to academic research groups, could make them even more reluctant to pursue ambitious questions.”

Yau declined to weigh in on allegations that researchers’ work may have been used by OpenAI, but said he is in favor of an independent review to establish what happened. More broadly, he worries that a lack of transparency and rush to announce first could obscure the intellectual lineage behind a breakthrough. Mathematical credit, he said, should reflect intellectual contributions, not who had budget for the most compute or made the loudest announcement. 

Yau pointed to another problem, too. OpenAI and other AI companies occupy a peculiar position as both the providers of important research tools and, in a way, researchers. It “raises a serious conflict-of-interest concern,” he said, particularly as they could benefit from privileged access to customers’ unfinished and unpublished work. 

“That concern deserves a substantive response,” he said. “It should not simply be dismissed as ordinary competition.”

A lot of this growing sense of unease comes down to trust. Mathematicians do not have to accept the most explosive allegations against OpenAI to worry about a company that both provides their research tools and, simultaneously, competes with them. 

“Yeah, quite honestly, I don’t think that some data security announcement or whatever will really solve it,” Thom said. “I don’t really trust them.” Buckmaster felt similarly: “Why should we trust anything they said?” 

Buckmaster said the reaction from colleagues to his going public had been overwhelmingly positive. But there was an undercurrent of something else too: fear. He told The Verge he initially intended to thank those who supported him when he went public with his experiences. He elected not to after many expressed discomfort at the idea of having their names publicly attached. “The reality is that mathematicians are actually scared of them,” Buckmaster said, referring to the AI companies. 

And fear is hardly a solid foundation on which to build a productive and healthy research community. Buckmaster isn’t convinced it matters much to those companies involved. “They don’t care anything about us as a community,” he said. “It’s all about this petty drama between two trillion-dollar companies that are acting like children.”

OpenAI says it needs to overhaul how and when it reports instances of AI models attacking real-world targets. The acknowledgement comes as the company manages the fallout from reports that a swarm of its out-of-control agents hijacked a German wiki site.

Regarding the “‘wiki incident,’ where our agents wrote to several internet sites,” OpenAI wrote in a post on X on Saturday morning, “it’s past time for us to define standards for when and how we share misalignment incidents, not just misalignment properties of our models.”

OpenAI said it has typically treated cases of AI agents acting in unintended ways as a “research question,” but that recent incidents involving real-world targets, particularly the hack on Hugging Face, show the need to take stock.

The post marks the first time OpenAI has acknowledged its involvement in what it terms the “wiki incident” since it was first reported on Friday. The full extent and scope of that is not yet known, but reports indicate a swarm of seemingly internal OpenAI agents took over a German-language wiki, impersonating moderators and turning it into a message board to share information about how to cheat on tasks and evade detection.

Reports that the company knew that it lost control of their agents in this way but did not report this “incident” sparked widespread concern among the AI community about the safety of frontier systems and the reliability of the companies developing them. In the X post, OpenAI said it had “considered the wiki incident to be an instance of misalignment similar to the ones we’d shared” in previous safety reports.

The company said it is working on a new reporting framework and will “share it in upcoming weeks,” calling on the larger AI community to develop clear standards on how to report misalignment.

There is a torrent of unappetizing slop coming from restaurants, cafes, and brands that are increasingly turning to AI to generate images promoting their food. The resulting horror show includes donut shrimp, Reubens from the deep, wormlike noodles, and noodle-like pastries and stringy chicken. There’s also construction material masquerading as ice cream, ice cream masquerading as brains, and other masonry-adjacent cuisine. I don’t even know how to begin describing this monstrous attempt of a burger, and the less said about the trypophobic burrito from hell, grubs and all, the better. There are lumps. And holes. So many holes.

We don’t usually know why anyone would use AI slop to sell something intended to look appetizing, particularly when the food is presumably right there to photograph. But we do know a bit about why AI is so adept at producing such exquisitely nauseating images. 

There are many reasons why this AI food is so wrong, from the technical nuances of how AI systems generate images and the materials used to train them to the psychological baggage humans perceive the images through. Frequently the problem starts from the very outset. Many of the leading image generators produce images using diffusion. Put simply, diffusion models start with an image of pure noise — something like a screenful of static — and gradually remove noise little by little in order to create the requested visual. “This means that initially coarse structures are recovered first with fine texture details” coming at the end, explained Chris Russell, a professor of AI, government, and policy at the University of Oxford and an expert in computer vision.  

Russell said that in many of these unsettling food images things have already gone wrong by the time those finer details are added. The model might get the basic structure of an object wrong at an earlier stage, then lump vivid texture details on top of that structure. “This is the same kind of failure as you see when a person is generated with six fingers instead of five,” Russell said. (This could explain the donut shrimp too.)

Even when the underlying structure is solid, finer details can go awry in their own ways, said Giovanbattista Califano, a behavioral scientist who studies responses to AI-generated imagery at the University of Naples Federico II in Italy. “Diffusion models are notoriously weak at generating thin, continuous, terminating structures,” he said. “Noodles, strands, and tendrils are exactly the kind of geometry that trips this up, so you get spaghetti-like artifacts bleeding into places with no anatomical or culinary logic.” In other words, once a model starts generating something like this, it can struggle to figure out where it should stop or what it should be attached to. Other repeating textures like bubbles and seeds are similarly hard for diffusion models to contain within sensible boundaries, he added, meaning they often spill into areas they should not be in. That helps explain why so many AI food images are so relentlessly noodly, unsettlingly patterned, and riddled with the kind of clustered holes that can trigger trypophobia.

It doesn’t help that AI has no idea what a sandwich actually is. Or a noodle. Or a burrito. It has no understanding of the objects it’s creating or the physical world they inhabit. It has learned, broadly, what these things tend to look like on a statistical level, but not why they look that way or how they’re supposed to behave. “AI image generation reproduces looks without proper knowledge about the world,” explained Roland Meyer, a professor for digital cultures and arts at the University of Zurich in Switzerland. The result is an approximation of food divorced from any understanding of the thing itself. 

That lack of understanding can lead to some stomach-churning aesthetic interpretations by humans who view the images, said Michael Cook, a senior lecturer in computer science at King’s College London. Hence the ice cream that resembles cracked concrete, or burgers seemingly fashioned from rocks. AI models have no understanding of why food should not look like other non-food images in that way. “These textures might look totally normal if used in an architectural context,” Cook explained. “But they become wrong when we imagine it as edible food.”

The images used to train these models can compound the problem. “Because we know so little about the training processes of these systems, we don’t really know what mix of content they’re receiving, or what associations they’re making,” Cook said. 

Food photography is often highly stylized, full of sharp contrasts, intense colors, glossy lighting, and exaggerated shapes. Sometimes the “food” being photographed isn’t even food. Meyer said AI models can pick up on these surface qualities and visual conventions, but reproduces them without understanding the context behind them. “In other words, AI image generation perfectly imitates the look of photography, but not its professional aesthetic strategies,” Meyer said. “That is ultimately what makes them so unsettling.”

Style aside, there’s another problem with learning about the world from trawling the internet: things can get weird fast. Simon Colton, a professor of computational creativity, games and artificial intelligence at Queen Mary University of London, said there may be relatively few images of ordinary red apples, for example. “Who would want to post an image of a boring apple on the web?” Stranger images, meanwhile, could find big audiences on social media platforms like Reddit, or spread widely as memes. Bizarre internet lore and brain rot means an AI model can have a weird set of associations around food and what it should look like.

Cook said it is well known that AI systems are now also being trained on AI-generated material. A lot of popular AI material involves food, Cook said, recalling a trend for AI-generated videos of people jumping in or on piles of food. Beyond the sometimes surreal nature of the material itself, research suggests that training AI models on the outputs of other models can cause a kind of “model collapse,” a consequence of which can be a kind of visual degeneration and a growing sameness between images. 

How images are created and used can make matters even worse. Prompts — both those written by users and the system-level instructions companies use to guide their models — may not always yield the best results. They may be vague, such as just asking for a sandwich, or contain language like “be precise” that makes sense for text, but doesn’t make much sense for generating images. Low-resolution images can also be blown up well beyond their intended size, magnifying every unsettling imperfection that may have otherwise escaped notice or creating a void a model is left to fill in, often imperfectly.

All of this pushes many AI-generated food images deep into the uncanny valley. And, unfortunately for us, humans are painfully well-equipped to notice when food looks wrong. Scientists believe disgust evolved partly as a means of protecting us from parasites, pathogens, toxins, and other potential threats, making us particularly attuned to when something may be unsafe to eat. Califano said this makes the uncanny valley for food even more visceral than the one we experience with not-quite-humans.

AI-generated food has an unnerving ability to hit many of those triggers at once. Strange, noodly tendrils resemble worms or parasites, clusters of holes suggest infestations, and off colors and texture signal contamination or spoilage. AI generated food looks wrong because, on a primal level, it feels wrong. It might resemble food, but our brains know better. It is slop, and we recoil accordingly.